A method of and an apparatus for three-dimensionally localizing light emitting marker entities of unknown orientation and unknown position in a sample are known from Manuel F. Juette et al.: “Three-dimensional sub-100 nm resolution fluorescence microscopy of thick samples” in Nature Methods, Vol. 5 No. 6, June 2008, p. 527-529. This paper discloses a method named biplane (BP) FPALM which combines a double-plane detection scheme with fluorescence photo-activation localization microscopy (FPALM) enabling three-dimensional sub-diffraction resolution. The z-position of the light emitting molecules is determined from the light intensity distributions over two detection planes onto which the light emitted by each single molecule is imaged and which correspond to two focal planes arranged at a known distance in z-direction. Depending on the actual position of a particular single molecule in z-direction, the emitted light intensity distributions over the different detection planes show different intensities and patterns allowing to determine the initially unknown z-position. In x- and y-directions in parallel to the focal planes, the position of each single molecule is determined in a way generally known from methods including FPALM, PALM, Stochastic Optical Reconstruction Microscopy (STORM) and PALM with Independently Running Acquisition (PALM IRA). This way principally includes fitting a two-dimensional Gaussian intensity distribution to the detected intensity distributions over the detection plane and defining the centre of the Gaussian distribution as the position of the molecule in x- and y-directions. Manuel F. Juette et al. do not care for any effects due to dipole characteristics of the molecules in emitting light.
From Erdal Toprak et al.: “Defocused orientation and position imaging (DOPI) of myosin V” in PNAS, Apr. 25, 2006, vol. 103 no. 17, p. 6495-6499, it is known that the centroid of a fluorophore can be determined within 1.5 nm accuracy from its focussed image through fluorescence imaging with one-nanometer accuracy (FIONA), and that, if, instead, the sample is moved away from the focus, the point-spread-function depends on both the position and three-dimensional orientation of the fluorophore, which can be calculated by defocused orientation and position imaging (DOPI). By switching back and forth between focussed and defocused imaging, DOPI allows for getting the centroid and the orientation of light emitting entities known to be located in a particular plane. The orientation of the marker entities is obtained from the emitted light intensity distribution of the defocused images of the marker entities; whereas their lateral position in the known plane is determined from the centre of the emitted light intensity distribution in the focussed image. The light emitting marker entities are either fluorophores, i.e. fluorescent molecules or quantum dots.
From Jörg Enderlein et al.: “Polarization effect on position accuracy of fluorophore localization” in: OPTICS EXPRESS, Vol. 14, No. 18, Sep. 2, 2006, p. 8111-8120, it is known that the intensity distribution of a light emitting molecule does not only depend on its position in space, but also on its three-dimensional orientation. Thus, the position determination usually done by fitting at two-dimensional Gaussian (x-y vs. photon number) to the emission intensity distribution may not result in the correct position of the light emitting molecule. In case of molecules placed in water on a glass surface, i.e. at a known z-position, the maximum shift of the centre position determined in this way using a 1.4 N.A. objective, however, was only 16 nm. With a smaller N.A. this position error should even be smaller as it is pointed out that the position accuracy for intermediate inclination angles of the dipole orientation of the light emitting molecules decreases with increasing N.A. Further, it is indicated that, if a dye is able to wobble around its attachment point during image exposure, thus emulating an isotropic emitter, the resulting image will be symmetric with respect to the actual position of the dye, and a 2-D Gaussian fitting will yield better FIONA accuracy than for any of the fixed dipole orientations. Jörg Enderlein et al. explicitly only regard conventional epi-fluoroscence microscopy and lateral positioning accuracy for molecules within the objective's focal plane. Studying the impact of molecule orientation on the position accuracy in other cases is told to be the topic of further studies.
There still is a need of methods of three-dimensionally localizing light emitting marker entities of unknown orientation and unknown position in a sample, and an apparatus for three-dimensionally localizing light emitting molecules of unknown orientation and unknown z-position in a sample in a sample, which provide for accurate x- and y-positions of the marker entities in the sample independently of their actual orientation and their actual z-position.